To make ds^2=ds¹^2 we may consider the following equations:[denoted by SET A]:(del_f1/del_p)^2+sin^2(f1)(del_f2/del_p)^2= (del_f3/del_p)^2+(del_f4/del_p)^2 ---------- (A1)(del_f1/del_q)^2+sin^2(f1)(del_f2/del_q)^2= (del_f3/del_q)^2+(del_f4/del_q)^2 --------- (A2)del_f1/del_p del_f1/del_q+ Sin^2(f1) del_f2/del_p del_f2/del_q =del_f3/del_p del_f3/del_q+ del_f4/del_p del_f4/del_q------------- (A3)If SET A has solutions for the functions f1,f2,f3 and f4 we arepassing from relation (1) to relation (2) by coordinatetransformation[ds^2 is preserved and it is being carried from onemanifold to another ]